Hyperbolic P-Y Criterion for Cohesive Soilsdeveloped by Matlock (1970), Reese and Welch (1975), Evans and Duncan (1982), Gazioglu and O’Neill (1984), Dunnavant and O’Neill (1989),

Jordan Journal of Civil Engineering, Volume 1, No. 1, 2007

- 38 -

Hyperbolic P-Y Criterion for Cohesive Soils

Robert Y. Liang1), Ehab S. Shatnawi2) and Jamal Nusairat3) 1) Professor, Dept. of Civil Engineering, The University of Akron, Akron, OH 44325-3905, [email protected]

2) Graduate Research Assistant, Dept. of Civil Engineering, The University of Akron, Akron, [email protected] 3) Project Manager – Research, E.L. Robinson, 6000 Memorial Drive, Dublin, OH 43017, [email protected]

ABSTRACT

Drilled shafts have been frequently used as a foundation to support lateral loads. The p-y method of analysis has been widely used for predicting the behavior of laterally loaded drilled shafts. The existing p-y criteria for cohesive soils are divided into soft or stiff clays, on the basis of a limited number of lateral load test results. Currently, there is no p-y criterion developed for cohesive intermediate geomaterial. In this paper, a hyperbolic equation for p-y curve is presented for cohesive soils and intermediate geomaterials. Based on 3-D FEM simulation results, a new empirical equation is presented for calculating the initial tangent to p-y curve. The proposed hyperbolic p-y criterion is verified by using the results of six full-scale lateral load tests on fully instrumented drilled shafts with diameters ranging from 0.76 m to 1.83 m in the geo-medium ranging from soft clays to intermediate geomaterial. The proposed hyperbolic p-y criterion is shown to be capable of predicting the loaddeflection and bending moments of the laterally loaded shafts for the six cases studied in this paper.

KEYWORDS: p-y criterion, Cohesive soils; Intermediate geomaterial, Lateral loads, Drilled shaft.

1. INTRODUCTION

Drilled shaft foundations are commonly used to resist

axial and lateral loads applied to structures, or to stabilize slopes. There is a number of different approaches for analyzing the behavior of laterally loaded drilled shafts, and the most widely employed is the p-y approach developed by Reese and his coworkers. The p-y method is based on the numerical solution of beam-on-elastic foundation, where the structural behavior of a drilled shaft is modeled as a beam and the soil-shaft interaction is represented by discrete, non-linear springs characterized by p-y curves.

A number of p-y curves for clays have been developed by Matlock (1970), Reese and Welch (1975), Evans and Duncan (1982), Gazioglu and O’Neill (1984), Dunnavant and O’Neill (1989), Hsiung and Chen (1997)

and Yang and Liang (2005). These existing p-y curves were developed based on a limited number of model or field lateral load tests on piles or drilled shafts. Furthermore, Yang and Liang (2005) have shown that the existing Reese and Welch (1975) and Gazioglu and O’Neill (1984) p-y criteria do not work well for the lateral load tests that they studied. The accuracy and applicability of the existing p-y curves for clays can be further validated or improved by using additional lateral load test results that have become available since their original developments.

The advancement of computer technology has made it possible to study lateral soil-drilled shaft interaction problems with the rigorous finite element method. Brown and Shie (1990) have conducted a series of three-dimensional finite element analyses on the behavior of single pile and pile group by using an elastic soil model. Brown and Shie derived p-y curves from finite element analysis results and provided some comparison with the Received on 7/10/2006 and Accepted for Publication on

18/12/2006.

Hyperbolic P-Y Criterion… Robert Y. Liang, et al.

- 39 -

empirical design procedures in use. Bransby and Springman (1999) utilized the two-dimensional finite element method to find load-transfer relationships for translation of an infinitely long pile through undrained soil for a variety of soil-constitutive models. Yang and Jeremić (2002) performed a finite element study on pile behavior in layered elastic-plastic soils under lateral loads and generated p-y curves from the finite element results. It was found that the finite element results generally agree well with centrifuge data.

The objective of this paper is to present a unified p-y criterion for cohesive soils and intermediate geomaterials by using hyperbolic mathematical formulation. The 3-D finite element parametric study results of laterally loaded drilled shafts in clay are used to develop empirical equations for calculating two important parameters in the hyperbolic p-y formulation: initial tangent to p-y curve, ki, and ultimate resistance, Pult,. A total of six full-scale fully instrumented lateral load test results are used to validate the proposed p-y criterion in predicting the load-deflection and bending moment of the drilled shafts under lateral loads.

The use of a hyperbolic function, given by Equation (1), as a p-y curve for sand, has been demonstrated by Kim et al. (2004) in their study of model tests in the Nak-dong River sand.

ultp

y

iK

1y

p+

= (1) where

p=force per unit shaft length (F/L), y=lateral displacement of shaft (L), Ki =initial subgrade reaction modulus of soil (F/L2)

and Pult=the ultimate reaction force per unit length of shaft (F/L).

In this paper, the hyperbolic function is suggested for constructing p-y curves for both soft and stiff clays as well as for intermediate geomaterial under short-term static loading. The methods to compute Ki and Pult are based on FEM simulation results and are discussed in the sections below.

2. BACKGROUND Given below is a brief review of existing equations

for calculating the two key parameters in the hyperbolic p-y function.

Initial Tangent to P-y Curve

By fitting the subgrade reaction solution with the continuum elastic solution for the beam on an elastic foundation, Vesic (1961) provided an elastic solution for the modulus of subgrade reaction, Ki as follows:

12/1

4

21

65.0

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−=

pIpE

EDEiK

ν (2)

where E = modulus of elastic materials, ν = Poisson’s

ratio, D = beam width, and EpIp = flexural rigidity of beam.

Bowles (1988) suggested to double the value of Ki in Equation (2) for piles under lateral loading, since the pile would have contact with soils on both sides. However, in reality, soils do not fully contact with the piles when lateral loads are applied. Based on field test data, Carter (1984) modified Vesic’s equation as follows to account for the effect of pile diameter:

12/1

4

)21(

0.1

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−=

pIpE

ED

refD

EDiK

ν (3)

where the reference pile diameter, Dref = 1.0 m, EpIp =

flexural rigidity of the piles or drilled shafts. As noted in FEM Modeling Section in this paper, the effect of Poisson's ratio on Ki by Carter (1984) seems to contradict to the FEM parametric study results. Ultimate Resistance, Pult

Based on a wedge failure mechanism, Reese (1958) provided an equation for estimating Pult, near the ground surface as follows:

2.83(2 )uult u

S zp S z DD

γ ′= + + (4)


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Table 1. Maximum Bending Moment at Different Loading Level for the Six Cases.

Max. Bending Moment (kN.m) Prediction Error Site

Lateral Load (kN) Proposed Reese/Matlock Measured Proposed Reese/Matlock 1601 3101 3470 1750 0.77 0.98 1868 3812 4243 2691 0.42 0.58 2313 5014 5487 4586 0.09 0.20

LOR-6

2580 5676 6171 5918 0.04 0.04 53 48 55 50 0.04 0.10 Slat Lake 98 93 114 90 0.03 0.26

1335 4678 5624 2427 0.93 1.32 1780 6881 8194 4312 0.60 0.90 2225 9165 10992 9619 0.05 0.14 2670 11488 13952 12105 0.05 0.15 2759 11973 14537 13000 0.08 0.12

CUY-90

3560 16699 20339 29063 0.43 0.30 22 37 38 28 0.33 0.37 45 77 78 58 0.33 0.34 67 118 119 91 0.29 0.30 90 159 162 124 0.28 0.31

134 236 253 190 0.24 0.33 180 320 352 351 0.09 0.00 224 406 448 431 0.06 0.04 269 494 544 521 0.05 0.04 343 651 705 694 0.06 0.02

CDOT

394 756 812 776 0.03 0.05 89 736 750 790 0.07 0.05

165 1349 1501 1452 0.07 0.03 267 2206 2284 2407 0.08 0.05 334 2759 2901 2917 0.05 0.01 400 3310 3527 3598 0.08 0.02 476 3951 4173 4236 0.07 0.01 538 4467 4884 4970 0.10 0.02 614 5103 5552 5411 0.06 0.03 689 5736 6223 6045 0.05 0.03

JEF-152

761 6327 6944 6468 0.02 0.07 178 200 203 163 0.23 0.25 445 560 568 407 0.38 0.40 667 900 907 667 0.35 0.36 890 1220 1268 1190 0.03 0.07 1112 1539 1647 1684 0.09 0.02 1334 1860 2041 2051 0.09 0.01 1512 2100 2421 2264 0.07 0.07

WAR-48

1690 2340 2784 2416 0.03 0.15


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Fig. 1: 3-D FEM Model.

Based on the flow-around failure theory for clay at a

great depth, Pult for in-depth clay is given as:

DSp uult 11= (5) Later, Matlock (1970) suggested computing Pult, by

using the smaller one of the values given by the equations below:

DuSz

D

Jz

uSultp ⎟⎟⎠

⎞⎜⎜⎝

⎛+

′+=

γ3 (6)

DSp uult 9= (7) where γ′ = average effective unit weight from ground

surface to the depth z under consideration, z = depth of the p-y curve, Su = undrained shear strength at depth z, D = diameter of the drilled shaft, J = 0.5 for a soft clay and J=0.25 for a medium clay. A value of 0.5 is frequently used for J. 3. FEM MODELING Initial Tangent Ki

The commercial ABAQUS finite element program is used for modeling the soil-drilled shaft interaction, as shown in Fig. 1. The drilled shaft is modeled as a

cylinder with elastic material properties. The solid elements C3D15 and C3D8 available in ABAQUS were used to develop mesh representation for shaft and clay, respectively. Surface interface technique is employed to simulate the soil-shaft interface. Since the determination of initial tangent to p-y curve constitutes the primary objective of this part of FEM study, only the elastic response of clay is the main concern of this part of the parametric study. Effect of Elastic Modulus of Soils, Es

The effect of elastic modulus of soils, Es, is studied by varying it from 5,000 kPa to 35,000 kPa. Other pertinent parameters are kept as constant as follows: D=1m, Ep=2.0×107 kPa,ν s=0.3. The FEM computed results are plotted in Fig. 2 (a), from which one can see that a power function fits the relationship between Ki and elastic modulus of the soil. Effect of Shaft Diameter, D

The effect of shaft diameter is investigated by varying the diameter from 1 m to 4 m. Other pertinent parameters are kept as constant as follows: Ep=2.0×107 kPa, Es=2.0×104 kPa,ν s=0.3. The Ki generated at a depth of 2 m is shown in Fig. 2 (b). It can be seen that Ki increases linearly with the increase of the shaft diameter.


- 42 -

Fig. 2: Effects of Shaft and Soils Parameters on Ki.

0

10000

20000

30000

40000

50000

60000

70000

80000

0 1 2 3 4 5Diameter (m)

K i (k

Pa)

depth= 2m

y = 87573x-0.0653

93000

94000

95000

96000

97000

98000

99000

100000

101000

102000

103000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4Poisson Ratio

K i (k

Pa)

FEM Result

Power fit (FEMResults)

y = 94549x-0.029

y = 47003x-0.028

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 5 10 15 20 25

Ep (2× 107 kPa)

K i (k

Pa)

ES= 1.0E5ES= 5.0E4Power (ES= 1.0E5)Power (ES= 5.0E4)

(a)

(c) (d)

y = 1.4486x0.9521

R2 = 0.9901

y = 4.705x0.8271

R2 = 0.9998

y = 6.8403x0.7826

R2 = 0.9783

0

5000

10000

15000

20000

25000

30000

35000

0 5000 10000 15000 20000 25000 30000 35000 40000Elastic Modulus of Soils (kPa)

K i (k

Pa)

depth= 1m

depth= 2m

depth= 3m

(b)

y = 15893x0.1246

R2 = 0.9669

y = 8090.8x0.2112

R2 = 0.9836

0

5000

10000

15000

20000

25000

0 1 2 3 4 5Depth (m)

K i (

kPa)

Es = 20000 kPa

Es= 10000 kPa

R2 = 0.9974

0

20000

40000

60000

80000

100000

120000

0 20000 40000 60000 80000 100000 120000Ki (kPa)- Emperical Predicted

Ki (k

Pa)-

FEM

Y= X

(e) (f)


- 43 -

Fig. 3: Ultimate Resistances vs. Depth.

0

50

100

150

200

250

0 2 4 6 8 10 12 14Depth (m)

ultim

ate

resis

tanc

e (k

N/m

)

Matlock(1970)

FEM

soft clay (Su= 10kPa, D= 2m)

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12 14 16Depth (m)

ultim

ate

resis

tanc

e (k

N/m

)

Matlock(1970)

FEM

Medium soft clay (Su=20kPa,D=2m)

0

500

1000

1500

2000

2500

0 2 4 6 8 10Depth (m)

ultim

ate

resis

tanc

e (k

N/m

)

Matlock(1970)

FEM

Stiff clay (Su= 200, D= 2m)

(a)

(b)

(c)


- 44 -

Fig. 4: Soil Profile and Shaft Dimension at Ohio LOR-6 Test Site.

Ground Surface

1.04

m

Inclinometer Pipe

Ep=30 Gpa

1.83

m

2.44

m

2.44

m

1.83 m

2@ 0.31 m

0.92

m

0.61 m

Steel Pipe

1.89

m

9.82

m

0- 0.9 Brown sand, silt, clay 220 0.005 20

0.9- 1.8 Brown sand, silt, clay 241 0.004 21

1.8- 3 Gray weathered clay shale

311

0.005

22

3.0- 4.6 Gray weathered clay shale 690 0.003 22

4.6-6 Argillaceous clay shale.

1033

0.001

22

6- 10 Argillaceous clay shale 2067 0.001 22

10- 12

Shale, dark-gray, firm, fissile, broken and jointed.

2067 0.001 22

Depth (m) Soil Description Su (kPa) ε50 γ (kN/m3)

#18 Bar

0.92 m

1.22 m

Section A-A

A A


- 45 -

Effect of Poisson’s Ratio of Soils, νs The Poisson’s ratio for cohesive soil is varied from

0.1 to 0.35, while other pertinent parameters are kept as constant as follows: D=1.0 m, Ep=2.0×107 kPa, Es=1.0×105 kPa. The Ki generated at a depth of 1 m is shown in Fig. 2 (c), where a power function can fit the data well. It is noted that in Carter’s empirical equation (Carter, 1984), an increase in Poisson's ratio leads to an increase in Ki. The present FEM results show that Ki decreases with an increase in Poisson's ratio. Effect of Elastic Modulus of Shafts, Ep

The effect of elastic modulus of shafts, Ep, is studied by varying it from 2.0×107 kPa to 4.0×108 kPa, while other parameters are kept as constant as follows: D=1m, Es=1.0×105 kPa and 5.0×104 kPa, ν s=0.3. Fig. 2 (d) shows the relationship between Ki and Ep . It can be seen that a power function fits very well the relationship between Ki and Ep. Effect of Depth, Z

The relationship between initial tangent of p-y curve and depth is also investigated by varying the depth from 1.0 m to 4.0 m. Other pertinent parameters are kept as constant as follows: D=1m, Ep=2.0×107 kPa,ν s=0.3. The FEM results are computed for two values of Es (10,000 kPa and 20,000 kPa) as shown in Fig. 2 (e), from which one can see that a power function can also fit the relationship between Ki and the depth. Suggested Empirical Equation for Ki

Based on the parametric study presented in the previous section, the following conclusions may be drawn: a) Ki and the following variables exhibit a power

relationship: the modulus of soils, the modulus of a shaft, depth and Poisson’s ratio of a soil.

b) Ki increases linearly with an increase in shaft diameter. A regression analysis on data from the FEM

parametric study is carried out. An equation for predicting initial modulus of subgrade reaction is fitted to match Ki values obtained from the FEM parametric

study. As shown in Fig. 2 (f), the empirical equation can be derived as follows.

031.0036.1078.0

016.0 )/()/(943.0−−

= pssrefref EEDDZZiK ν (8) where Zref = 1.0 m and Dref =1.0 m.

Ultimate Resistance, Pult

The strength of saturated clay is usually characterized by undrained shear strength, Su; therefore, clay is modeled as a simple Von Mises material in the FEM simulation.

The finite element model used to obtain the ultimate resistance is the same as the one used to obtain Ki. The drilled shaft with a diameter of 2 m is modeled as an elastic material, while the undrained shear strength of cohesive soils is varied from 10 kPa to 200 kPa. The ultimate resistances computed from finite element analyses are shown in Fig. 3 (a) to (c) for three representative values of Su. It can be seen that the results of finite element analyses agree generally well with those deduced from the Matlock’s method. The ultimate resistance of in-depth clay from FEM is generally larger than 9SuD, but smaller than 11SuD. Therefore, 10SuD is adopted in this paper. The ultimate resistance of clays can be calculated by using the smaller one of the values given by the following equations:

DuSzD

Jz

uSultp ⎟⎟⎠

⎞⎜⎜⎝

⎛+

′+=

γ3 (9)

DSp uult 10= (10)

4. CASE STUDIES Six lateral load tests are employed to validate the

proposed p-y criterion for cohesive soils by comparing the measured and predicted load-deflection curves, and the deflection vs. depth curves.


- 46 -

Fig. 5: Comparison of Predicted and Measured Load-Deflections of Ohio LOR-6 Test.

Fig. 6: Comparison of Predicted and Measured Deflections vs. Depth of Ohio. LOR-6 Test.

0

500

1000

1500

2000

2500

3000

0 1 2 3 4 5 6 7Deflection at Shaft Top (cm)

Late

ral L

oad

(kN)

MeasuredProposed p-yWeltch& Reese p-y

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5 3 3.5 4Deflection (cm)

Dept

h (m

) Predicted at 222kNPredicted at 1100kNPredicted at 2580kNMeasured at 222kNMeasured at 1100kNMeasured at 2580kN


- 47 -

`

Fig. 7: Soil Profile and Pile Detail at Salt Lake International Airport Test (After Rollins et al., 1998).

Ground Surface

0.61

m

Bottom of the Pile

Strain Gage

0.61

m

0.91

m

1.52

m

Steel P(f)

7.62

m

0- 0.8 Silt W/ Sand (ML) 100

0.8- 2.2 Lean Gray Clay(CL) 75 25

2.2- 3.1 Light Gray Sandy Silt (ML) 40

3.1- 4.8 Poorly Graded, Light Brown sand (SP)

Ф=38° K=5000 kN/m3

4.8- 5.5 Lean Gray Clay(CL) 50 25

5.5-8.0 Gray Silt (ML) 65 10

Depth (m) Soil Description Su (kPa) PI(%)

0.61

m

0.91

m

0.91

m

1.5 (

c)

Positioning Device

Strain sensing pile

0.4

m

Gravel Fill (Excavated)

0.305 m

Ep (avg.)=62 GPa


- 48 -

Fig. 8: Comparison of Predicted and Measured Load-Deflection Curves of Salt Lake International Airport.

In addition to deflection prediction, the maximum

moments of drilled shafts under different loading levels predicted by using LPILE based on the proposed p-y criterion and other existing p-y criteria are compared with the corresponding maximum moments based on strain gage readings. The moment prediction errors, defined as the absolute value of moment difference divided by the measured moments, are summarized in Table1. Ohio LOR-6 Test (Liang, 1997)

The soils at the test site are composed primarily of silt clay, underlain by gray clay shale. The soil profile at the LOR-6 test site is presented in Fig. 4.

The undrained shear strength of clay is correlated to undrained elastic modulus as follows (U.S. Army Corps of Engineers, 1990):

ucS SKE = (11) where Kc is a correlation factor. The value of Kc as a

function of the overconsolidation ratio and plasticity index, PI, is estimated to be 500.

The geometry and dimension of test shaft as well as the instrumentation layout are shown in Fig. 4. The diameter of the shaft in clay is 1.22 m, while the diameter of the shaft socket in the shale is 0.92m. Inclinometer casing and strain gages were installed inside the shaft.

Fig. 5 shows the comparison of the predicted and measured load-deflection curves. It can be seen that the predicted load-deflection using the proposed hyperbolic p-y criterion agrees very well with the measured values. The Reese and Welch (1975) p-y criterion overpredicts the deflections. A comparison of the predicted and measured deflections vs. depth is shown in Fig. 6.

The average maximum bending moment prediction errors using the proposed p-y criterion is 0.33 as it can be calculated from Table 1. It is less than 0.45, the average prediction error by using Reese and Welch p-y criterion (1975).

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6 7Deflection at Shaft Top (cm)

Late

ral L

oad

(kN)

MeasuredProposed p-yMatlock p-y


- 49 -

Fig. 9: Soil Profile and Shaft Dimension at CUY-90 Test Site.

Inclinometer Pipe

43 m

Depth (m) Soil Description Su

(kPa) ε50

×10-3 γ

(kN/m3)

0 - 2 FILL: Dense black fine to coarse sand, little fine to coarse gravel, trace SILT 53 7 19

2 - 4 FILL: Dense black fine to coarse sand, little fine to coarse gravel, trace SILT 52 7. 19

4 - 12

Stiff to very-stiff gray SILTY CLAY, trace fine to medium SAND, horizontal structure Medium-stiff to stiff gray SILTY CLAY, trance fine GRAVEL, few lenses of silt

65 7 9

12 - 16 Stiff to very-stiff gray SILTY CLAY, trace fine to coarse SAND, few seams and lenses of SILT 83 6 11

16 - 30 Very-stiff to hard, stiff to very-stiff gray SILTY CLAY, trace fine to coarse sand, few seams and lenses of SILT

110 6 11

30 - 36 Very-stiff to hard gray CLAY, little fine to coarse sand, face fine GRAVEL. 213 5 10

36 - 38

Dense gray fine to medium sand, little CLAYEY SILT, trace fine GRAVEL Dense gray fine to coarse GRAVEL, some fine to coarse sand, trace CLAYEY SILT

310 5 9

38 - 43 Dense gray fine to coarse GRAVEL, some fine to coarse SAND, trace CLAYEY SILT 255 4 11

Es=500 Su

24#18 Bar

1.83m

Ep(avg.) =30GPa

0.6 m

1.4 m


- 50 -

Fig. 10: Comparison of Predicted and Measured Load-Deflection Curve of Ohio CUY-90 Test.

Fig. 11: Comparison of Predicted and Measured Deflections vs. Depth of Ohio CUY-90 Test.

0

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20Deflection at Shaft Top (cm)

Late

ral L

oad

(kN)

MeasuredProposed p-yReese & Welch p-y

0

5

10

15

20

25

30

35

40

45

50

-2 0 2 4 6 8 10 12 14Deflection (cm)

Dept

h (m

) Predicted at 3000kNPredicted at 3500kNMeasured at 3000kNMeasured at 3500kN


- 51 -

Fig. 12: Soil Profile and Shaft Dimension at Colorado I-225 Clay Site.

Salt Lake International Airport Test (Rollins et al., 1998)

The test pile was 0.305m I.D. closed-end steel pipe with a 9.5-mm wall thickness driven to a depth of approximately 9.1 m. The elastic modulus of the steel was 200 GPa, and the minimum yield stress was 331 MPa. Prior to conducting the lateral pile load testing, inclinometer casing and strain gauges were placed inside the pile. The pile was then filled with concrete. The compressive strength and the elastic modulus of the concrete at the time of testing were 20.7 MPa and 17.5 GPa, respectively.

The soil profile at the test site as well as the pile instrumentation detail are presented in Fig. 7. The soils

near the ground surface are clays and silts with undrained shear strength typically between 25 kPa and 50 kPa. Some layers showed undrained shear strength of 100 kPa. The underlying cohesionless soil layer consists of poorly graded medium-grained sands and silty sands. Based on EM 1110-1-1904, for PI=25, Es of cohesive soils can be estimated to be 1000Su.

The proposed hyperbolic criterion and the Matlock (1970) criterion are used to generate two sets of p-y curves for the clay layers. Reese et al. (1975) p-y criterion is used to generate the p-y curves for the sand layers. The LPILE analysis results by using these p-y curves are compared with the measured load-deflection curve in Fig. 8. The proposed p-y curves provides good

Ground Surface

5@ 0

.91

m

Inclinometer Pipe

Ep(avg.)=60GPa for the top 0.6m and 34.5GPa for the rest of the shaft

Strain Gage

Steel Pipe

0.7(b)

4.59

m

(0-2m) Fill, Silty Clay

152 91200 18.7

(2-3.8m) Native silty clay

86 51600 18.4

(3.8-4.8m) Native silty clay

105 6300 19.8

Soil Discription Su (kPa) E(kPa) γ (kN/m3)

1.(b

)

0.3 m

#8 Str

#4 Str


- 52 -

Fig. 13: Comparison of Predicted and Measured Load-Deflection Curves of CDOT Clay Site. match with the measured load-deflection curve. Also, its bending moment prediction errors are less than that of Matlock (1970) p-y criterion prediction. Ohio CUY-90 Test (Liang, 2000)

The soils near the ground surface are mainly composed of silts, soft to stiff clays. Deposits in great depth are shale with trace of gravel. The test shaft is 45.0 m long with an embedded length of 43 m. The lateral load was applied at a point 0.6 m above the ground surface. The diameter of the test shaft is 1.83 m, reinforced with 24 bars, 57mm in diameter, and a built-up beam. Fig. 9 shows the soil profile at the site as well as the details of reinforcement inside the shaft.

Fig. 10 and Fig. 11 show the predicted and measured load-deflection curves and the deflection-depth curves, respectively. It can be seen that the proposed p-y criterion can predict the load-deflection of the drilled shaft much

better than the Reese and Welch (1975) p-y criterion. At five different loading levels out of the six shown in

Table 1, the maximum bending moment prediction errors calculated based on the proposed p-y criterion results are less than those calculated based on the Reese and Welch (1975) p-y criterion. Colorado I-225 Test (Nusairat et al., 2004)

The soil profiles at the test site with the soil parameters interpreted from pressuremeter test as well as the instrumentation of the test shaft are presented in Fig.12.

The shaft is relatively short, with embedment length of 4.59 m. Therefore, the resistance of the shaft tip is a significant component of the overall lateral resistance. The comparisons between the predicted and measured load-deflection curves are shown in Fig. 13. A discrepancy is observed, which may have been contributed by the shear resistance at the base of the shaft .

0

50

100

150

200

250

300

350

400

450

0 0.5 1 1.5 2 2.5 3 3.5Deflection at Shaft Top (cm)

Late

ral L

oad

(kN)



- 53 -

Fig. 14: Soil Profile and Shaft Dimension at Ohio JEF-152 |Test Site.

This is another case proving that the maximum

bending moment predicted using the proposed p-y criterion matches the measured value better than the prediction using Reese & Welch (1975) p-y criterion as calculated in Table1. Ohio JEF-152 Test (Nusairat et al., 2006)

The soil profile and the undrained shear strength and modulus of elasticity of the soil interpreted from pressuremeter test are summarized in Fig. 14. The depth to the intermediate geomaterial is 7.6 m from the ground surface as shown in Fig. 14, where the instrumentation of the test shaft is also presented.

The proposed hyperbolic p-y criterion and Reese and

Welch (1975) p-y curves for stiff clay are used to generate the p-y curves as input in the LPILE program to predict the load-deflection curve of the test shaft. Fig. 15 shows the predicted and measured load-deflection curves. The predicted and measured deflection vs. depth curves are compared in Fig. 16. The comparison of the predicted and measured maximum bending moment is given in Table 1. It can be seen that the proposed p-y criterion allows LPILE program to predict the measured data very well.

Ohio WAR-48 Test (Nusairat et al., 2006) The test site is located on SR 48 over Clear Creek in

Warren County, Ohio. The test shafts were part of retaining wall supporting the roadway. The drilled shafts

4(a)

7.6m

1.83m

0.3m

1.06m

0.61m

Inclinometer casing

Top of Intermediate Geomaterial

1.73 m dia. casing

0.61m

Ground Surface

Silty clay

Red mudstone, water flowing, slickensided, decomposed

344.5 105000 21

At 2.0 m from the Top of Intermediate Geomaterial Red mudstone, water flowing, slickensided, highly weathered, RQD=65%

448 225000 21

Su (kPa) E(kPa) γ (kN/m3)

0.91m OD Casing

2 4#11


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Fig. 15: Comparison of Predicted and Measured Load Deflection Curves of Ohio JEF-152 Test.

Fig. 16: Comparison of Predicted and Measured Deflection vs. Depth Curves of Ohio JEF-152 Test.

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50Deflection at the load of application point (cm)

Late

ral L

oad

(kN)


0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25Deflection (cm)

Dept

h (m

)

Predicted at 400kN

Predicted at 760kN

Measured at 400kN

Measured at 760kN


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Fig. 17: Soil Profile and Shaft Dimension at Ohio War-48 Test Site.

were excavated by using the “dry” method, with temporary casings for excavation support. The total length of the drilled shaft is about 7.02 m, with 1.52 m extension above the ground surface for load application. The subsurface stratigraphy encountered during drilling of the 1.22 m diameter shafts consisted of shale from the ground surface to the bottom of the shafts.

Field rock dilatometer tests were conducted at this site. The limiting pressure, undrained shear strength and the modulus of elasticity, interpreted from the dilatometer tests, are summarized in Fig. 17 together with instrumentation details. The reinforcement of the shaft was 12 -35 mm and 6 -44.4 mm bars with a concrete cover of 7.6 cm.

The lateral loads were applied 0.6 m below the top of the shaft in increments of 222.5 kN. The maximum lateral load reached was 1780 kN.

For comparison, the proposed hyperbolic criterion, Reese and Welch (1975) stiff clay criterion and Reese (1997) weak rock criterion were used to generate p-y curves. The load-deflection curves predicted by LPILE program with these p-y curves are shown in Fig. 18. Fig. 19 shows the predicted and measured deflection vs. depth. It can be seen that the proposed hyperbolic criterion provides the best match.

The maximum bending moment prediction by using both p-y criteria are almost the same as it can be seen in Table1.

Bottom of Shaft

5.5m

Ground Surface

6 #14 (Tension Side Only) 12 #11

PL Su Em ( kPa) ( kPa) ( kPa)

(0-1m) 12,815 700 165000

(1-2m) 11,713 800 180000

(2-5.5m) 15,916 1000 410000

1.22 m

Highly weathered shale

1.52

m

0.6

m


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Fig. 18: Comparison of Predicted and Measured Load Deflection of Ohio WAR-48 Test.

Fig. 19: Comparison of Predicted and Measured Deflection vs. Depth Curves of Ohio WAR-48 Test.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.5 1 1.5 2 2.5 3 3.5 4Deflection at the load of application point (cm)

Late

ral L

oad

(kN)

Measured

Proposed p-y

Reese & Welch p-y

0

1

2

3

4

5

6

7

8

9

-0.5 0 0.5 1 1.5 2 2.5 3Deflection (cm)

Dept

h (m

)

Predicted at 180 kN

Predicted at 1110 kN

Measured at 180 kN

Measured at 1110 kN


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5. CONCLUSIONS A hyperbolic p-y criterion is developed for cohesive

soils and intermediate geomaterial .The 3-D FEM simulation results are used to develop a new empirical equation to calculate initial tangent to p-y curve, Ki. The

proposed p-y criterion is verified based on comparisons with six full-scale lateral load test results conducted in soft clay to intermediate cohesive geomaterial. The proposed p-y criterion is shown to be capable of predicting the behavior of these test shafts under lateral loading.

REFERENCES

Bowles, J. E. (1988). Foundation Analysis and Design, 4th

Edition, McGraw Hill, New York, 1004. Bransby, M.F. and Springman, S. (1999). “Selection of load-

transfer functions for passive lateral loading of pile groups.” Computers and Geotechnics, 24(3):155-184.

Brown, D. and Shie, C. (1990). “Numerical experiments into group effects on the response of piles to lateral loading.” Computers and Geotechnics, 10 (3): 211-230.

Carter, D. P. (1984). A non-linear soil model for predicting lateral pile response. Rep. No. 359, Civil Engineering Dept., Univ. of Auckland, New Zealand.

Dunnavant T.W. and O’Neill M.W. (1989). “Experimental p-y model for submerged stiff clay.” J. Geotech. Engrg., 115(1), 95-114.

Evans, L. T. and Duncan, J. M. (1982). Simplified analysis of laterally loaded piles. UCB/GT/82-04, University of California Berkeley.

Gazioglu S.M. and O’Neill M.W. (1984). “Evaluation of p-y relationships in cohesive soil. Analysis and Design of Pile Foundations.” Proceedings, San Francisco, California, 192-213.

Hsiung Y. and Chen Y. (1997). “Simplified method for analyzing laterally loaded single piles in clays.” J. Geotech. Geoenviron. Engrg., 123(11), 1018-1029.

Kim, B.T., Kim, N., Lee, W.J., and Kim, Y.S. (2004). “Experimental load-transfer curves of laterally loaded piles in Nak-Dong River sand.” J. Geotech. Geoenviron. Engrg., 130(4), 416-425.

Liang, R.Y. (1997). Pressuremeter to predict the lateral load capacity of drilled shafts on slopes. A research report submitted to the Ohio Department of Transportation and

FHWA, June,1997. Liang, R.Y. (2000). Instrumentation, monitoring and testing

at the CUY-90-15.24 central viaduct project. A research report submitted to the Ohio Department of Transportation and FHWA, June.

Matlock, H. (1970). “Correlation for design of laterally loaded piles in soft clays.” 2nd Offshore Technology Conference, Houston, Texas, 577-594.

Nusairat, J., Liang, R. and Engel, R. (2006). Design of rock socketed drilled shafts. A research report submitted to the Ohio Department of Transportation and FHWA, July.

Nusairat, J., Liang, R., Engel, R., Hanneman, D., Abu-Hejleh, N. and Yang, K. (2004). Drilled shaft design for sound barrier walls, signs, and signals. Final Report, CDOT-DTD-R-2004-8, Colorado Department of Transportation.

Reese, L.C. (1958). “Discussion of soil modulus for laterally loaded piles.” by B. McClelland and J.A. Focht, Jr., Transactions, ASCE, 123: 1071-1074.

Reese, L. C., Cox, W. R. and Koop, F. D. (1974). “Analysis of laterally loaded piles in sand.” Proc. of 6th Offshore Tech. Conf., Houston, TX, Vol. 2, p. 473-483.

Reese, L.C. and Welch, R.C. (1975). “Lateral loading of deep foundations in stiff clay.” J. Geotech. Engrg. Div., ASCE, 101(7), 633-649.

Reese, L.C., Cox, W.R. and Koop, F.D. (1975). “Field testing and analysis of laterally loaded piles in stiff clay.” Seventh Annual Offshore Technology Conference, Dallas, Texas, 671-690.

Rollins, K., Peterson, K. and Weaver, J. (1998) “Lateral load behavior of full-scale pile group in clay.” J. Geotech. Geoenviron. Engrg., 124 (6), pp. 468-478, June.

U.S. Army Corps of Engineers (1990). Engineering Manual


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(1110-1-1904) Engineering and Design: Settlement Analysis.

Vesic, A. S. (1961). “Beam on elastic subgrade and the Winkler hypothesis.” Proc. 5th Int. Conf. Soil Mechanics and Foundation Engineering, Paris, Vol. 1, p. 845-850.

Yang, K. and Liang, R. (2005). “Lateral response of large diameter drilled shafts in clay.” Proc. 30th Annual

Conference on Deep Foundations, Deep Foundation Institute, 115-126.

Yang, Z. and Jeremić, B. (2002). “Numerical analysis of pile behaviour under lateral loads in layered elastic-plastic soils.” Int. J. Numer. Anal. Meth. Geomech. 26:1385-1406.

Documents

Hyperbolic P-Y Criterion for Cohesive Soilsdeveloped by Matlock (1970), Reese and Welch (1975), Evans and Duncan (1982), Gazioglu and O’Neill (1984), Dunnavant and O’Neill (1989),